The Welfare Effect of a Consumer Subsidy with Price Ceilings:

The Case of Chinese Cell Phones*

Ying Fan�

University of Michigan,

CEPR and NBER

Ge Zhang�

Amazon Web Services

December 16, 2021

Abstract

Subsidies to consumers may cause firms to charge higher prices, which offsets consumer benefits from

subsidies. We study a subsidy program design that mitigates such price increases by making products’

eligibility for a subsidy dependent on firms’ commitment to price ceilings. To quantify the importance of

such competition for eligibility, we develop a structural model and an estimation procedure that accom-

modate binding pricing constraints. We find that competition for eligibility mitigates the price increases

arising from the subsidy and even leads to a reduction in prices for some products. It improves consumer

and total surpluses while limiting government subsidy payments.

Keywords: subsidy, price ceiling, competition for eligibility, cell phone

JEL classification: L1, D4, H2

1 Introduction

Governments worldwide often use consumption subsidies or taxes — two sides of the same coin — to

stimulate or discourage certain types of consumption. Examples include solar panel rebates and tobacco

excise taxes. Policy makers also use consumption subsidies to help targeted disadvantaged consumers (e.g.,

food stamps and child-care subsidies) and constitute a major component of government expenditure. How-

ever, by shifting demand to the right, such subsidies may lead to higher prices, and the consumer surplus

gain from the subsidy may be smaller than the government subsidy payments.

*We thank Steven Berry, Philip Haile, and seminar participants at Yale University for their constructive comments. Wethank the Cowles Foundation for Research in Economics, the Michigan Institute for Teaching and Research in Economics, andthe NET Institute for their generous financial support.

�Department of Economics, University of Michigan, 250 Lorch Hall, Ann Arbor, MI 48109-1220; yingfan@umich.edu.�2121 8th Avenue, Seattle, WA 98121-2607; gzhan@amazon.com.

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In this paper, we study a subsidy program where firms compete to have their products eligible for a

subsidy. Such competition motivates firms to lower prices and thus improves consumer surplus. Specifically,

the program includes a bidding process where each participating firm proposes a list of products and a

price ceiling for each proposed product. The program committee evaluates the proposals and determines

the set of products eligible for the consumer subsidy. It is common knowledge that the price ceiling is a

crucial determinant of a product’s chance of becoming eligible. After the bidding, firms must set a subsidized

product’s retail price no higher than its respective price ceiling. To increase the probability of becoming

eligible for the subsidy, a firm may have an incentive to commit to a low price ceiling. Thus, the ex-ante

competition for subsidy eligibility may put downward pressure on prices, mitigating the price increase that

would otherwise result from the consumer subsidy. Examples with similar policy designs include the infant

formula rebate by the “Women, Infants, and Children” (WIC) program (Oliveira et al. 2010; Davis 2014)

and the Low-Income Subsidy (LIS) for Medicare prescription drug coverage (Decarolis et al. 2020) in the

US.1

The subsidy program we study is called “Home Appliances Going to the Countryside” (henceforth,

HAGC). Implemented in China from 2008 to 2012, it provided a rebate of up to 13% of the product price to

consumers from the countryside if they purchased eligible home appliances and electronics. By the end of

2012, the HAGC program subsidized 298 million units of products that were sold for a total of 720.5 billion

CNY.2 The total government spending on HAGC subsidies was around 90 billion CNY. In this paper, we

focus on the subsidy for cell phones.

We quantify the welfare effect of the HAGC program on firms, subsidized consumers, and unsubsidized

consumers. Unsubsidized consumers may also be affected by the program because firms set the same price for

all consumers, and the program may lead to changes in prices. To highlight the role that firms’ competition

for subsidy eligibility plays in shaping the subsidy program’s welfare implications, we further decompose the

overall welfare effect into those due to the subsidy itself, the set of eligible products, and the price ceilings.

To clarify, due to the lack of data on the list of participants or their submitted price ceilings, we cannot

estimate the bidding process. As a result, we do not study what if the eligibility competition were removed.

Instead, we study what if the outcomes of the eligibility competition (i.e., the eligibility set and the price

ceilings) were removed as a decomposition of the overall welfare effect of the subsidy program.

To this end, we set up a structural model of consumer demand and firm pricing. We specify a random-

coefficients discrete-choice demand model that allows consumers to differ in preferences and subsidy eligibility.

We model the firms as strategically choosing prices to maximize profits subject to the constraint that they

must price a subsidized product no higher than its price ceiling. As mentioned, we do not model or estimate

1WIC assists low-income families and their children in purchasing healthy foods. In the infant formula rebate program byWIC, eligible households receive infant formula vouchers from state WIC agencies. The vouchers apply to a single infant formulabrand in each state, as determined by a bidding process. Specifically, the manufacturer that offers the WIC state agency thelowest predicted net price, as determined by the manufacturer’s wholesale price in the previous year minus the rebate, wins theexclusive contract. In the LIS program, only plans with a premium below the average premium in their market are eligible forlow-income enrollees to obtain the full premium subsidy.

2CNY is short for Chinese Yuan, the local currency in China. The exchange rate was 1 USD = 6.23 CNY at the end of 2012.

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the bidding process but instead take the eligible product set and the price ceilings as given. To address

concerns about the selection in the bidding outcomes (i.e., the eligible product set and the price ceilings),

we control for firm, region, and time fixed effects in our model specification. We consider it reasonable to

assume that the product/region/time-specific transitory shocks are unobservable to firms when they bid and

to the evaluation committee when deciding on the winning bids.

The existence of (binding) pricing constraints is exactly why the competition for eligibility can mitigate

price increases under subsidy and thus improve consumer surplus. However, such binding constraints imply

that some firms’ profit-maximization problem is a constrained one, which invalidates the usual supply estima-

tion procedure based on the first-order optimality conditions (e.g., Berry et al. (1995)). Instead, we develop a

procedure for marginal cost estimation (and counterfactual simulations) that accommodates binding pricing

constraints. The basic idea is to first estimate marginal cost coefficients and the empirical distribution of

marginal cost shocks using the sample of firms without eligible products, free of a sample selection bias given

the aforementioned assumption on unobservables; then repeat a “draw-and-verify” procedure to approximate

the distribution of marginal costs for the firms with binding pricing constraint(s). We explain this method

in detail in Section 5.2.

We assemble a dataset on the HAGC-eligible cell phones and their price ceilings from government doc-

uments, and link it to Chinese cell phone sales data from July 2007 to June 2013, covering the lifespan

of the HAGC program. Using these data, we estimate demand and marginal cost parameters. Based on

the estimated model, we conduct three counterfactual simulations to quantify the program’s effects and to

highlight the role of firms’ competition for eligibility in mitigating price increases and improving consumer

surplus.

We find that competition for eligibility mitigates price increases due to the subsidy program and even

leads to a reduction in prices for some products. For example, the prices of the eligible products with binding

price ceilings in the data are, on average, 10.05% lower than a scenario without a subsidy. Because prices

are strategic complements, even though other products’ prices increase due to the subsidy program, the

increases are smaller than those under the same subsidy without price ceilings.

Overall, we find that the HAGC subsidy program increases the consumer surplus and producer surplus by,

respectively, 3.07 and 2.77 billion CNY, which are 68% and 61% of the total government subsidy payments.

However, if there were no price ceilings resulting from competition for eligibility, these gains would be

2.76 billion and 2.97 billion CNY or 61% and 66% of the total government subsidy payments, respectively,

indicating that the price ceilings improve consumer surplus in both level and share of the subsidy. If

competition for eligibility were removed altogether (thus both the eligibility set and the price ceilings were

removed), these percentages would become 95% and 37%. However, the predicted total subsidy payments

would be six times the actual payments and might not be financially feasible. Moreover, focusing on the rural

consumers, who are the targeted population of the program, we find that their gains would decrease from

31% of the total subsidy payments to 22% if the design of competition for eligibility were removed. Overall,

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these results indicate that firms’ competition for subsidy eligibility in the program benefits consumers and

increases total surplus while limiting the required government subsidy payments and that it also increases

the effectiveness of the subsidy in helping the targeted population.

Our paper contributes to the literature on the welfare effects of consumption tax and subsidy policies.

Many papers point out the role of market power in subsidy pass-through (or tax incidence). See, for example,

Weyl and Fabinger (2013) for a theoretical discussion, Cabral et al. (2018) on Medicare Advantage subsidies,

Polyakova and Ryan (2021) on Affordable Care Act subsidies, Pless and van Benthem (2019) on solar panel

subsidies in California, and Sallee (2011) on hybrid car tax credits. However, there is little work on the

role of price ceilings or other price controls in subsidy or tax policies. Our paper adds to the literature by

highlighting the role of particular policies designed to tackle what hinders consumer gains from the subsidy –

the price increase arising from the subsidy. Our paper suggests that such policy designs can benefit consumers

while limiting government expenditure.

By studying a subsidy program targeting disadvantaged consumers in a developing country, our paper

contributes to the literature on the evaluation of subsidy programs in less developed economies. Among

the studies on the HAGC subsidy program, Chen et al. (2015) assess the impact of household technology

on health outcomes, while Tewari and Wang (2020) estimate its impact on female labor force participation.

Like these papers, we investigate a subsidy program that aims to help disadvantaged consumers. Unlike

most of these papers, we quantify the direct impacts of the subsidy program on consumption and welfare,

rather than the indirect impacts on socioeconomic outcomes.

Our paper is also related to the empirical research on cell phone or smartphone markets. For example,

Wang (2020) studies how entry affects product portfolio choices in the Chinese smartphone market, Fan and

Yang (2020) study the welfare effects of endogenous product choices and competition in the US smartphone

market, and Zhu et al. (2015) and Sinkinson (2020) study exclusive contracting for early iPhones. We

complement these papers by studying a consumer subsidy in this industry.

We complete the literature review by comparing our supply model and some models in the trade and

environmental economics literature. In these models, firms also face certain constraints, and Lagrange

multipliers are included in optimality conditions as (often nuisance) parameters. For example, in Goldberg

(1995), some firms face export quotas, and each constrained firm is subject to one constraint when choosing

prices for all its products. In our case, however, a firm faces one (different) price ceiling for each of its subsidy-

eligible products, leaving no variation for us to identify the (hundreds of) Lagrange multiplier parameters.

Instead, we develop an estimation procedure as explained in Section 5.2.

The remainder of this paper proceeds as follows. Section 2 provides background information on the

HAGC subsidy program. Section 3 describes our data. Section 4 sets up our structural model, and Section

5 discusses our estimation procedure and reports the estimates. In Section 6, we conduct counterfactual

simulations for welfare analysis. We conclude in Section 7.

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2 Background

2.1 HAGC Subsidy Program Overview

Home Appliances Going to the Countryside (HAGC) was a subsidy program effective between 2008 and

2012 in China. This program provided subsidies to targeted consumers if they purchased eligible home

appliances and electronics. The main goals were to improve the quality of life for the relatively low-income

rural population and to stimulate domestic consumption when China’s exports declined severely due to

the 2008 financial crisis. The HAGC program was first launched as a pilot program in three provinces

in December 2007, expanded to twelve more provinces in November 2008, and eventually to all the other

provinces in mainland China in January 2009. It was first terminated in the three pilot provinces in December

2011, then in the next twelve provinces in November 2011, and finally in all the remaining provinces in

January 2013.3 The HAGC subsidy program was a sizable program with total government spending of 90

billion CNY on 298 million units of subsidized products sold for a total of 720.5 billion CNY by the end of

2012.

Four categories of products were subsidized nationwide, including color TVs, refrigerators, and cell phones

since the beginning of the pilot program, and washing machines since 2009. Each province was allowed to

choose several additional product categories such as air conditioners, water heaters, computers, microwave

ovens, and electromagnetic cookers.

In this paper, we focus on the cell phone market for two reasons. First, the cell phone category was

one of the four categories available in all provinces, for which we have richer data than the regional product

categories. As will be explained later, we exploit cross-province and cross-time variations in the set of

subsidy-eligible products for estimation. Second, there were concurrent additional subsidy programs for the

other three national categories, but not for cell phones. For example, for TVs, refrigerators, and washing

machines, there was a trade-in promotion in 2009-2011 and a subsidy program for energy-saving products

in 2012-2013.

The subsidy was in the form of a rebate. If a consumer was eligible for the subsidy and purchased a

qualified product, she paid the same retail price as ineligible consumers but would receive a rebate of 13%

of the retail price up to a maximum rebate of 130 CNY for a cell phone.4 Consumers were very likely to

be aware of products’ eligibility status and effective prices because the HAGC program was one of the most

important subsidy policies in China around 2010, the public media widely and repeatedly reported on the

HAGC program, and there was an HAGC label on the package of each eligible product.

3The different ending times ensured that residents in each province were eligible for the subsidy for the same length of time.4Each consumer was allowed for up to two rebates per year on cell phone purchases, which was unlikely to be a binding

restriction for most consumers.

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2.2 Product Eligibility and Incentives to Curb Prices

A critical component of the HAGC program was the firms’ competition for subsidy eligibility. The set

of products eligible for the subsidy was determined by a bidding process. There were six rounds of bidding

from 2008 to 2012. In each round, each participating firm proposed a list of products and a corresponding

price ceiling for each product, together with a list of provinces.5 If a product was eventually chosen to be

eligible for the HAGC subsidy in a province, the price ceiling became a constraint to the product’s firm when

choosing its retail price in the province.

A committee from China’s Ministry of Finance and Ministry of Commerce evaluated these proposals based

on product characteristics, firm characteristics (e.g., previous sales and customer service in each province),

and, most importantly, the price ceilings. Although the evaluation criteria might be opaque, it was common

knowledge that submitting a lower price ceiling, ceteris paribus, would increase the chance of a product being

chosen for the program. Such competition for subsidy eligibility curbed firms’ incentives to raise prices under

the subsidy.

Figure 1 presents a hypothetical example of a firm’s original proposal and winning proposal. Multiple

products from multiple firms could be eligible for the subsidy simultaneously. The evaluation committee

might decline some of the products and some of the provinces on a proposal while accepting the other

products and provinces as winners, but they would never impose a price ceiling different from that on the

proposal. While we do not observe the original proposals that firms submitted (i.e., the left panel of Figure

1), the winning proposals (i.e., the right panel of Figure 1) were publicly announced and observable to

researchers.

Figure 1: A Hypothetical Example of a Proposal

There are some details about the pricing restrictions that are worth noting. First, a product was not

subject to a price ceiling in a province if it was not a subsidy-qualifying product in the province. Second,

although a subsidized product was subject to the same price ceiling across eligible provinces and months,

firms could and did set different retail prices across provinces and months. Third, retail prices were the

same for all consumers in the same province and month, no matter whether the consumer was eligible for

the subsidy or not (Section 2.3). Fourth, proposed price ceilings in the cell phone category must be below

1,000 CNY in 2008-2009 and below 2,000 CNY in 2010-2012.

5The list of provinces must be the same for all the listed products, and the price ceiling for a listed product must be thesame for all the listed provinces.

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2.3 Consumer Eligibility and Hukou

Roughly 0.9 billion Chinese citizens, or 70% of the national population, were eligible for the HAGC

subsidy. A consumer was eligible if and only if she had a so-called “Agricultural Hukou”. Hukou is a

household registration system used in mainland China where the household register is issued per family.

Historically, Hukou officially identified a person as a permanent resident of an area: agricultural Hukou meant

one’s permanent residence was in a rural area, and non-agricultural Hukou meant permanent residency in an

urban area. However, due to rapid urbanization and massive migration within China, Hokou was no longer

a good description of whether a person mostly lived and worked in a rural or urban area by the time of the

HAGC program (as will be shown in the next section).

Nonetheless, the Chinese government often assigns social benefits based on agricultural or non-agricultural

Hukou status (Wang 2014). One reason is that the government has the official record of Hukou information

for every citizen in mainland China. When the government implements a social benefit program, it is much

less time- and labor-consuming to verify Hukou status than income level and residence location. Another

reason is that the Hukou registration type (agriculture/non-agriculture) was given to a person at her birth

based on her parents’ Hukou types and thus is prohibitively difficult and costly to change in the short run.

Assigning benefits based on Hukou helps to prevent people from abusing benefits by taking actions to become

eligible for social programs. Due to these two reasons, the HAGC subsidy program used agriculture Hukou

as the eligibility criterion for simplicity despite the aim to help low-income residents in the countryside, and

it is reasonable for us to assume that consumers did not change Hukou types in response to the HAGC

program.

Given the difference between Hukou and residence, we distinguish them in our analysis. While the

former distinction (agriculture vs. non-agriculture) determines the subsidy eligibility, the latter (rural vs.

urban residents, or population in a rural vs. urban area) is assumed to be relevant for consumer preferences

in the demand model. The significant variation in residence and Hukou proportions across markets helps

identify our demand model.

3 Data

Our cell phone sales data come from GfK, a leading market research company for consumer products.

The data set includes the universe of cell phones sold in mainland China between July 2007 and June 2013,

which spans six months before the HAGC program to six months after it. We observe the total number of

units sold and the average retail price for each cell phone product in every month in the sample and every

province in mainland China.

The price in the sales data is for a cell phone handset, excluding any promotion or service charge set by

mobile carriers. Note that the majority of cell phone handsets in China were sold separately from a wireless

network service contract during the time of the data, according to industry analysis reports. Thus, we can

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make the reasonable simplifying assumption that the cell phone firms choose the final retail prices to the

end consumers in our model.

Key characteristics of each product are also available in the data set. Specifically, we observe whether a

product is a smartphone or a feature phone, whether it includes a camera, whether it includes a touch screen,

whether it supports the 3G network, whether it supports dual SIM, whether it has a “flip” or “slider” design,6

storage in gigabytes, camera resolution in megapixels, and handset size in inches. On the rare occasions of

missing characteristics data, we hand-collected the information from The List of Telecommunications Equip-

ment Approved for Network Access Licenses (Including Trial Approvals) (in Chinese) by China’s Ministry

of Industry and Information Technology and GSMArena.com.

Data on the winning proposals come from the China National Electronics Import and Export Corporation,

the HAGC subsidy program’s bidding agency. We observe the eligible products, their price ceilings, the

eligible provinces, and the effective dates for each bidding round. We then link the HAGC subsidy data to

the Chinese cell phone sales data by matching the product model name (and the eligible markets).

Data on demographics come from the National Bureau of Statistics of China (NBS). The NBS pro-

vides data on the numbers of rural and urban residents each year and province, but not by Hukou type.

One exception is that in the 2010 Population Census, the NBS provides the provincial-level data on four

types of residents: rural residents with agricultural Hukou, urban residents with agricultural Hukou, ru-

ral residents with non-agricultural Hukou, and urban residents with non-agricultural Hukou. Using these

data from the 2010 Census, we compute the conditional proportions Pr(agriculture Hukou |urban residents)

and Pr(agriculture Hukou | rural residents). We combine these province-level conditional proportions with

province/year-level data on the numbers of rural and urban residents to obtain our measure of the populations

of all four types in each province and each year.

We consider a province/quarter combination to be a market. A vast majority of consumers in China

bought cell phones from a local retail market during our sample period: online sales account for 8.75% of

the total sales units in our data. We drop online sales because our data source reports online sales only

at the national level without providing a breakdown at the province level. In the end, our sample consists

of 98,446 observations (product/province/quarters) from 728 markets (province/quarters). There are 3,457

distinct products and 205 distinct firms, among which 390 products and 20 firms are ever eligible for the

HAGC subsidy. See Appendix A for details on our sample construction.

Table 1 presents the summary statistics of sales units, retail price, and key characteristics at the obser-

vation level. The first four columns report summary statistics for the full sample, the fifth for subsidized

observations, and the last for observations with binding pricing constraints (i.e., the retail price equals the

price ceiling). From the table, we can see that the average of the subsidized products is lower than that of

the full sample for the retail price and across all product characteristics, indicating that the HAGC program

6“Flip” means that this cell phone has a flip, and the flip may include functions like a microphone, keyboard, or camera.“Slider” means that this cell phone has an orientation where the keypad is not visible, and it needs to be pulled or pushed outfor the keypad to be revealed.

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focused on low-end products. The existence of the 453 observations with binding pricing constraints shows

the effectiveness of firms’ competition for subsidy eligibility in mitigating price increases under subsidy and

improving consumer surplus. Since prices are strategic complements, they are likely to also put downward

pressure on other non-binding or unsubsidized products. We show and quantify these effects explicitly later.

Table 1: Summary Statistics of Cell Phone Sales and Characteristics

Overall Subsidized Binding

Variable Mean Std Min Max Mean Mean

Number of units sold 6,536 13,935 500 893,457 8,299 5,454Retail price (1,000 CNY) 1.00 0.63 0.11 3.00 0.59 0.61Smartphone (v.s. feature phone) 0.25 0.08 0.01Include camera 0.77 0.60 0.55Include touch screen 0.32 0.20 0.21Support 3G network 0.30 0.17 0.18Dual SIM card 0.13 0.07 0.25Design: flip 0.10 0.07 0.10Design: slider 0.17 0.15 0.10Storage memory (GB) 1.08 1.10 0.01 16.00 0.94 0.99Camera resolution (MP) 2.00 1.52 0.10 12.00 1.24 1.12Handset size (inch) 4.67 0.37 2.88 8.74 4.56 4.61

Number of observations 98,446 11,309 453

Figure 2 plots the histograms of the price ceilings and the ratios of retail prices to price ceilings for the

observations of the subsidized products. The upper panel shows the distribution of price ceilings in CNY.

The median, indicated by the vertical line, is 658 CNY. The distribution is skewed to the left, consistent with

the HAGC program’s focus on low-end products. There is bunching at or just below 1,000 CNY because

firms could not propose a price ceiling above 1,000 CNY in 2008 and 2009. The lower panel shows the

distribution of the ratios of retail prices to price ceilings, with a median of 82%. The observations on the

right end of the panel are those with binding pricing constraints or with prices close to their price ceilings.

Figure 3 shows the distribution of population proportions across markets. Each of the four panels

corresponds to a combination of a residence type (rural or urban) and a Hukou type (agriculture or non-

agriculture). For each market, the four percentages in the four panels add up to 100%.7 From the upper right

panel, we can see many markets with a sizable proportion of consumers living and working in an urban area

while being registered as agricultural Hukou. Therefore, it is important to distinguish these two different

categorizations of consumers. From the figure, we can also see significant variation in residence and Hukou

proportions across markets, which helps our demand estimation as subsidy eligibility depends on Hukou

while consumer tastes in our model depend on residence location.

7For example, in the Heilongjiang province in 2010, 40% of the total population were people with agricultural Hukou inrural locations, 5% for agricultural Hukou in urban, 10% for non-agricultural Hukou in rural, and the remaining 45% fornon-agricultural Hukou in urban.

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Figure 2: Histograms of Price Ceilings

Figure 3: Population Proportions by Hukou and Residence Location

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4 Model

4.1 Demand Model

We specify a random-coefficients discrete-choice demand model. There are four types of consumers

determined by their Hukou type (h = A for agriculture Hukou, and h = NA for non-agriculture Hukou) and

their residence location (l = R for being in a rural area, and l = U for being in an urban area). Consumers

with different Hukou types face different effective prices for products eligible for the HAGC subsidy. We

allow consumers with different residence locations to have different preferences for cell phones and different

price sensitivities. Preference is more likely to differ across residence locations than Hukou types because

factors that affect cell phone demand, such as how consumers use cell phones in daily life, are more related

to where they currently live and work than their household registration type in the government’s system.

Specifically, the utility that consumer i with Hukou h and residence l in province m and quarter t gets

from purchasing product j (produced by firm f(j)) is

uh,lijmt = ρl + βXj + αlimt(pjmt−bhjmt(pjmt)) + Firmdf(j) + Provincedm + Timedt + ξjmt + εijmt, (1)

where Xj is a vector of observable product characteristics, pjmt is the retail price, and bhjmt(pjmt) is the

subsidy amount, which depends on whether j is eligible for the subsidy in market mt, whether the consumer

is eligible for the subsidy, and the retail price of the product. Specifically, let Jmt and J emt represent,

respectively, the set of all products and the set of products eligible for the subsidy in market mt. For

consumers with non-agricultural Hukou (h = NA) or for products that are not eligible for the subsidy

(j ∈ Jmt \ J emt), bhjmt = 0. For consumers with agricultural Hukou (h = A) and eligible products (j ∈ J emt),

the subsidy is 13% of the retail price up to a maximum of 130 CNY. In sum, bhjmt(pjmt) = 1{h=A} ·

1{j∈J emt} ·min{pjmt, 1000} · 13%.

The random coefficient αlimt captures consumers’ heterogeneous price sensitivity and is assumed to follow

a normal distribution depending on consumer i’s residence location, i.e., αlimt = αl+σανi, where νi

iid∼ N(0, 1).

We also allow consumers’ general taste for cell phones, ρl, to differ by consumers’ residence location.

We allow for demand-side fixed effects Firmdf(j), Province

dm, and Timedt in the utility function (1) to

capture systematic differences across firms, provinces, and quarters. We also include the term ξjmt to capture

the unobservable demand shock at the product/province/quarter level.

Finally, the term εijmt captures consumer i’s idiosyncratic taste and is assumed to be i.i.d. across individ-

ual consumers and markets. We assume that εijmt follows a generalized extreme value distribution allowing

correlations across products. Specifically, we group products into three nests (smartphones, feature phones,

and the outside option) and allow for correlations in εijmt among products of the same nest. Let λ be the

nested Logit correlation coefficient. We normalize the utility of the outside option to be uh,li0mt = εi0mt.

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Define the mean utility of product j for consumers of type (h, l) in market mt as

δh,ljmt = ρl + βXj + αl(pjmt−bhjmt(pjmt)) + Firmdf(j) + Provincedm + Timedt + ξjmt, (2)

and let

µhijmt = σανi(pjmt−bhjmt(pjmt)). (3)

Then, the utility function (1) can be written as uh,lijmt = δh,ljmt + µhijmt + εijmt.

Let Jgmt be the set of products in market mt that belong to nest g, G(νi) denote the distribution of νi,

and (δh,lmt,pmt) be the collection of (δh,ljmt, pjmt) for all j ∈ Jmt. The probability that a consumer of type

(h, l) chooses product j of nest g in market mt is

sh,ljmt(δh,lmt,pmt) =

∫exp{(δh,ljmt + µhijmt)/(1− λ)}

Dλg (∑g′ D

(1−λ)g′ )

dG(νi), (4)

where

Dg =∑

j′∈Jgmt

exp{(δh,lj′mt + µhij′mt)/(1− λ)}.

We aggregate the consumer type-specific market share function to obtain the product/province/time level

market share as ∑(h,l)

τh,lmt sh,ljmt(δ

h,lmt,pmt), (5)

where τh,lmt is the population proportion of consumers of type h, l in market mt.

4.2 Supply Model

We describe the supply side by Bertrand competition. Firms with no eligible products solve a standard

profit maximization problem, while firms with eligible products choose prices subject to the price ceilings of

their eligible products.

Denote the product set of firm f by Jfmt and the set of its subsidized products by J efmt, and define

pfmt = (pjmt)j∈Jfmt to be the retail prices for firm f ’s products. We now rewrite the market share function

in (5) as sjmt(pfmt,p−fmt) where its dependence on non-price factors is absorbed in the subscription jmt.

Given the retail prices of the competitors in the market (p−fmt) and marginal cost mcjmt, firm f chooses

its prices pfmt to maximize its profit:

maxpfmt

∑j′∈Jfmt

(pj′mt −mcj′mt) sj′mt(pfmt,p−fmt), (6)

s.t. pj′mt ≤ pj′t for j′ ∈ J efmt.

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For a firm f without any eligible products, i.e., J efmt = ∅, the problem in (6) becomes an unconstrained

optimization problem.

The optimality condition gives that

∑j′∈Jfmt

(pj′mt −mcj′mt)∂sj′mt∂pjmt

+ sjmt = 0 for j 6∈ J efmt or pjmt < pjt, (7)

∑j′∈Jfmt

(pj′mt −mcj′mt)∂sj′mt∂pjmt

+ sjmt ≥ 0 for j ∈ J efmt and pjmt = pjt. (8)

In other words, for ineligible products or eligible products with non-binding price ceilings, the equation (7)

holds; for eligible products with binding price ceilings, however, the inequality (8) holds.

We assume the marginal cost is

mcjmt = γXj + Firmsf(j) + Provincesm + Timest + ωjmt, (9)

where Firmsf(j), P rovince

sm, T ime

st are supply-side fixed effects at various levels and ωjmt is the unobservable

marginal cost shock.

We complete this section with a discussion about the bidding process. Due to the lack of data on the

proposals that firms submitted but did not win, we do not observe the set of participants and their proposals

(products, price ceilings, and provinces). Therefore, we do not explicitly estimate the bidding process. To

rule out selection (on unobservable shocks) in subsidy eligibility, as determined by the bidding process, we

assume that marginal cost shocks are realized after the bidding process, i.e., the shocks are unobserved

to firms when submitting their bids and to the evaluation committee when choosing winning bids. This

timing assumption is reasonable because we include firm-, province- and time-specific fixed effects in the

marginal cost specification, and thus the shocks are only product/province/time-specific transitory ones.

Our estimation in Section 5 relies on this timing assumption.

5 Estimation

5.1 Demand Estimation

The demand estimation is a slight extension to that in Berry et al. (1995) (henceforth, BLP). Our market

share data are at the product/province/quarter level. While there are four types of consumers who differ

in preferences and subsidy eligibility and the overall market share is a weighted average of the type-specific

market shares, we can extend the inversion results in BLP to solve for the unobservable demand shocks ξjmt

as a function of parameters and data. Specifically, note that according to the definition of the mean utility

13

in (2), the four mean utility values have the following relation:

δNA,Rjmt = δA,Rjmt + αRbAjmt; (10)

δA,Ujmt = δA,Rjmt + (ρU − ρR) + (αU − αR)(pjmt − bAjmt);

δNA,Ujmt = δA,Rjmt + (ρU − ρR) + (αU − αR)pjmt + αRbAjmt.

Using (10), we can define the market share function in (5) as

sjmt(δA,Rmt ,pmt, τmt) =

∑(h,l)

τh,lmt sh,ljmt(δ

h,lmt,pmt), (11)

where τmt = (τA,Rmt , τNA,Rmt , τA,Umt , τ

NA,Umt ). The market share function in (11) is a function of δA,Rjmt but not

the mean utilities of the other three consumer types. Equaling (11) to the market share in data sjmt (for

all j ∈ Jmt), we can solve for the mean utility δA,Rjmt (smt,pmt, τmt, ρU − ρR, αR, αU ), where smt denotes the

collection of sjmt for all j ∈ Jmt. Then we have the estimation equation as:

δA,Rjmt (smt,pmt, τmt, ρU − ρR, αR, αU ) (12)

= ρR + βXj + αR(pjmt−bAjmt(pjmt)) + Firmdf(j) + Provincedm + Timedt + ξjmt.

Some taste parameters are allowed to differ across residence locations. However, our sales data are

not residence-location specific, so the identification of such taste differences depends on the variation of

rural/urban population proportions across provinces and time. Intuitively, consider two identical provinces

except that the percentage of rural residents is higher in province A than in province B. If the total market

share of high-priced products is smaller in province A than in province B, then such a data pattern indicates

that rural residents are more sensitive to price than urban residents.

We estimate the demand parameters using the Generalized Method of Moments. The prices and market

shares in the demand model are endogenous in the sense that they are correlated with ξjmt, the unobserved

component of mean utility. We use the following instrumental variables to deal with this endogeneity

issue. First, following the literature, we construct BLP instruments based on the characteristics of other

products of the same firm, or products of competing firms, or “close” products.8 Second, since the differences

between rural and urban tastes are identified by variations in the population proportions of consumer types,

our additional instrumental variables are the population proportions and their interactions with the BLP

instruments. The market size used in the demand estimation is 10% of the population in the corresponding

province and time, and our results are robust to alternative market size measures.

8Following Gandhi and Houde (2019), two products in the same market are “close” in a categorical characteristic if the twoproducts are in the same category, and “close” in a numerical characteristic if the difference between the two products is lessthan the standard deviation of that characteristic in that market.

14

5.2 Supply Estimation

The optimality conditions derived in Section 4.2 show that equation (7) holds for ineligible products or

eligible products with non-binding price ceilings, and inequality (8) holds for eligible products with binding

price ceilings. Consequently, we can back out the marginal costs for some products (i.e., marginal costs are

“point identified”), but there may be a set of marginal cost values that satisfy the optimality conditions for

the other products (“set identified”). In this section, we estimate the marginal costs for a subset of products

and the underlying marginal cost distribution for all products. In the counterfactual simulations in the next

section, we use the estimated marginal costs for the “point identified” observations; for the observations

whose corresponding marginal costs cannot be point identified, we draw marginal costs that are consistent

with both the underlying distribution of marginal cost and the observed outcome as an equilibrium.

A comparison of our approach to the existing ones in the literature is in order. As explained in the intro-

duction, different from Goldberg (1995) where a multi-product firm faces only one constraint, our firms face

one constraint for each observation of eligible products, leading to many Lagrangian multiplier parameters

to be estimated and no variation for identifying these parameters.9 We cannot follow the literature using

moment inequalities for estimation (e.g., Pakes et al. (2015)) either. Note that inequality (8) includes a set

of error terms (i.e., marginal cost shocks ωj′mt for all j′∈Jfmt), which do not enter the inequality in an

additively separable fashion. Moreover, the optimality condition (8) does not generally imply inequalities in

the form of cjmt ≤ mcjmt ≤ cjmt, where cjmt and cjmt are constants.10 As a result, a moment assumption

such as E(ωjmt) = 0 does not imply moment inequality conditions.

We now turn to our approach. Note that for an observation jmt, as long as its firm has any product j′ in

this market mt with a binding price ceiling so that we have inequality (8) for j′mt, we cannot back out mcjmt

even if the equation (7) holds for this jmt itself. Therefore, we partition the observations by firm/market

combinations: (A) observations of firms with no eligible products in the market: {jmt : J ef(j)mt = ∅}; (B)

observations such that some of the firm’s products are eligible in the market but none of the corresponding

price ceilings are binding: {jmt : J ef(j)mt 6= ∅, pj′mt < pj′t,∀j′∈J ef(j)mt}; (C) observations such that at

least one product of its firm in the market is both subsidized and has a binding pricing constraint: {jmt :

∃j′∈J ef(j)mt s.t. pj′mt = pj′t}.

For observations in both Samples (A) and (B), the equation (7) holds for all the products of the corre-

sponding firm f(j) in the market mt. Therefore, we can back out the marginal cost as

mcjmt = pjmt + [∆−1fmtsfmt]jmt,∀j∈Jfmt, (13)

where sfmt = (sjmt)j∈Jfmt and ∆fmt is a |Jfmt|×|Jfmt| matrix whose (j, j′) element is∂sj′mt∂pjmt

,∀j, j′∈Jfmt.

9Dubois and Lasio (2018) also study firm pricing facing price ceilings. In their setting, a product is sold in both unconstrainedmarkets (without price ceilings) and constrained markets (with price ceilings). The variation across such markets helps theidentification of the Lagrangian multipliers.

10Therefore, we cannot easily construct bounds for these marginal costs either.

15

We estimate the distribution of marginal costs as follows. Under the timing assumption explained at the

end of Section 4.2, the distribution of marginal cost shocks conditional on Sample (A) (i.e., observations

that belong to firm/markets where the firm has no eligible products in the market) equals the unconditional

distribution: F (ωjmt|jmt ∈ A) = F (ωjmt). Therefore, we can estimate the distribution F (ωjmt) using

observations in Sample (A). For these observations, we plug in the backed-out marginal costs from (13) into

the marginal cost specification (9) and estimate the marginal cost parameters (γ, ˆFirms

f ,ˆProvince

s

m,ˆTime

s

t )

using the Generalized Methods of Moments.11 The estimated marginal cost shocks ωjmt for jmt ∈ A are used

to estimate the distribution F (ωjmt). Note that although we can back out the marginal cost for observations

in Sample (B), we do not use these observations to estimate the distribution because they are selected. These

observations are from firms that price all subsidized products strictly below the price ceilings, a decision made

after observing the marginal cost shocks.

For observations in Sample (C), we draw the marginal costs that are consistent with both the estimated

underlying distribution of marginal cost and the observed outcome as an equilibrium. To do so, we proceed

with the following steps. For each firm/market fmt with observations in Sample (C), we simulate draws

of marginal cost shocks from the estimated distribution F (ωjmt). Denote such a draw as (ωrjmt)j∈Sample (C)

where ωrjmti.i.d.∼ F (·). We then compute the corresponding marginal costs as γXj + ˆFirm

s

f + ˆProvinces

m +

ˆTimes

t + ωrjmt and keep the draws such that these marginal costs satisfy all optimality conditions of this

firm/market.12 We repeat this process for all firm/markets in Sample (C).

To sum up, the procedure for estimating the supply model (and obtaining marginal cost draws for sample

(C) in counterfactual simulations) is as follows:

Step (i). Estimate marginal costs for Samples (A) and (B) using first-order conditions and demand

estimates, and denote the results by (mcA, mcB);

Step (ii). Estimate marginal cost coefficients and marginal cost shocks (ωA) using Sample (A) only;

Step (iii). Use ωA to estimate the empirical distribution of marginal cost shocks (F (ω));

Step (iv). Draw marginal cost shocks for Sample (C), as explained above. Denote the corresponding

marginal cost draws by mcrC , r = 1, ..., R, where R is the number of simulation draws.

Step (v). Use (mcA, mcB ,mcrC) to conduct counterfactual simulations.

We end this subsection with a discussion on the no-selection assumption. First, the underlying timing

assumption for the no-selection assumption is that the unobservable marginal cost shocks are realized after

the bidding process, and thus, the distribution of marginal cost shocks for observations that belong to

firm/markets where the firm has no eligible products in the market (i.e., Sample (A)) equals the unconditional

distribution. As argued in Section 4.2, we consider this timing assumption reasonable because we include

firm-, province-, and time-specific fixed effects in the marginal cost specification. The unobservable marginal

11We estimate the firm fixed effects for the 17 largest firms separately and a group of all other fringe firms. These 17 firmsaccount for 93.33% of the observations.

12In practice, if we draw all marginal cost shocks for a market, it is nearly impossible that they will satisfy the equations inthe optimality conditions. So, we draw shocks for the observations with binding constraints, compute the other shocks usingthe optimality equations, and then take all drawn or computed shocks to verify the optimality inequalities.

16

cost shocks are, therefore, transitory shocks at the product/province/time level and likely to be unknown

to firms when submitting bids and to the evaluation committee when choosing winning bids. Second, we

present summary statistics for Samples (A)–(C) separately in Appendix C and show that there are significant

overlaps in the observable product characteristics, price and sales across the three sub-samples. Though not

a proof for no selection on unobservables, the similarity in the observables is reassuring. Third, as explained

in the procedure above, we directly use the backed-out marginal costs for observations in Samples (A) and

(B) in our counterfactual simulations. The no-selection assumption is only relevant for drawing the marginal

cost shocks for Sample (C), which counts for only about 7% of all observations.

5.3 Estimation Results

Table 2 reports the demand estimation results. We allow the coefficients on effective price and the

constant term to be different between rural and urban consumers. The differences have the expected signs

and are significant. Compared to urban consumers, ceteris paribus, rural consumers are more sensitive to

price (perhaps because of their lower average income). They are also more likely to purchase a cell phone

(probably because fewer of them already own a cell phone). We allow for a random coefficient on price,

but its estimated dispersion is very small and statistically insignificant.13 The estimated coefficient for

the eligibility dummy is negative, probably because the HAGC products are mostly low-end products and

the dummy variable captures some unobservable features of these products. All the coefficients on favorable

product characteristics are positive and significant as expected.14 For example, to an average rural consumer,

upgrading from a feature phone to a smartphone is equivalent to a price decrease by about 96 CNY.

Table 3 reports the marginal cost estimation results using the same instrumental variables as the demand

estimation. We assume that firms maximize their profits from rural consumers rather than from all consumers

for two reasons. First, according to industry analysis reports, the major firms focused on expanding their

businesses for their low-end products in rural areas during the sample period, partially in response to the

HAGC program. Second, when we assume that a firm’s objective function is a weighted average of profits as

wπrural+(1−w)πurban, where πrural (or πurban) is the profit from rural (or urban) consumers, and estimate

both marginal cost coefficients and w as an additional coefficient, we obtain an estimate of w = 0.98.15

The estimation results show that marginal cost, as expected, is positively associated with all product

characteristics and significantly so with most ones. The characteristics that consumers care about most,

namely rear camera resolution and handset size, also have the largest marginal cost coefficients.

13Therefore, we assume the standard deviation of the random coefficient to be zero in the remainder of the paper.14The three continuous variables of characteristics, namely storage, rear camera resolution, and handset size, are normalized

to have an absolute value between zero and one so that the magnitudes of their coefficients are comparable to those of dummyvariables.

15The weight parameter w is identified by rural population proportion variations across markets.

17

Table 2: Estimation Results on Demand

Variable Est. S.E.

Constant: Rural -6.03*** (0.09)Constant: Urban - Rural -2.05*** (0.14)Effective Price: Rural -5.72*** (1.08)Effective Price: Urban - Rural 4.91*** (0.22)Price random coefficient std. 0.001 (0.72)Being eligible for subsidy -0.03*** (0.01)Smartphone (v.s. feature phone) 0.55*** (0.02)Include camera 0.84*** (0.05)Include touch screen 0.27*** (0.01)Support 3G network 0.23*** (0.01)Dual SIM card 0.04*** (0.01)Design: flip 0.47*** (0.02)Design: slider 0.43*** (0.01)Storage memory (normalized) 1.29*** (0.04)Camera resolution (normalized) 2.83*** (0.11)Handset size (normalized) 5.95*** (0.17)Nested Logit coefficient 0.26*** (0.01)Province, time, and firm dummies Yes

*** p<0.01., ** p<0.05, * p<0.10.

Table 3: Estimation Results on Marginal Cost

Variable Est. S.E.

Constant -1.03*** (0.028)Smartphone (v.s. feature phone) 0.32*** (0.005)Include camera 0.55*** (0.003)Include touch screen 0.005* (0.003)Support 3G network 0.04*** (0.003)Dual SIM card 0.04*** (0.003)Design: flip 0.32*** (0.004)Design: slider 0.33*** (0.004)Storage memory (normalized) 0.18*** (0.014)Camera resolution (normalized) 2.86*** (0.013)Handset size (normalized) 3.33*** (0.062)Province, time, and firm dummies Yes

*** p<0.01., ** p<0.05, * p<0.10.

18

6 Counterfactual Simulations

We conduct counterfactual simulations to quantify the welfare effect of the subsidy program and highlight

the role of competition for eligibility (which determines the price ceilings and the eligible product set).

In each simulation, we hold the set of products available in the market fixed.16 We draw marginal cost

shocks as described by Step (iv) in Section 5.2, solve for the new pricing equilibrium for each market, compute

the corresponding total government subsidy payments, consumer surplus, and producer surplus, and report

averages across simulation draws. We do so for all market/quarters with the HAGC program in place. We

use the bootstrap method for standard errors. Specifically, we repeat the above process for different draws

of the model parameters from the estimated distribution.

We conduct three counterfactual simulations where the subsidy rate for eligible purchases is the same

as in the data, i.e., 13% of the retail price up to a maximum subsidy of 130 CNY. Table 4 summarizes the

counterfactual designs. In the first counterfactual simulation (CF1), we simulate what would have happened

if there were no subsidy at all. The comparison of such simulation results to outcomes according to the data

gives us the overall effect of the HAGC subsidy program, i.e., the subsidy combined with firms’ competition

for subsidy eligibility, which restricts the subsidy to a set of eligible products and leads to a price ceiling

for each eligible product.17 In the second counterfactual simulation (CF2), we simulate what would have

happened if the same set of products as in the data were eligible for the subsidy but there were no pricing

ceilings. Comparing the outcomes from CF2 and those according to the data allows us to quantify the effect

of price ceilings. Note that we use CF2 for the purpose of decomposition and we do not consider it to be a

realistic subsidy policy because the eligibility and the price ceilings are jointly determined by the eligibility

competition. For example, if the government is looser on selecting winners, there should be both a larger

eligibility set and higher ceilings. In the third counterfactual simulation (CF3), we simulate the effect of an

alternative program where there is no competition for eligibility at all, i.e., all products were eligible for the

subsidy and there were no price ceilings. The comparison of its results to those in the data informs us about

the effect of having the design of the eligibility competition.

Table 4: Counterfactual Simulations

Counterfactual Eligible Price The comparison v.s. CF1product set ceilings gives the effect of . . .

Data Actual Actual Subsidy + eligible set + ceilingCF1 None NoneCF2 Actual None Subsidy + eligible setCF3 All None Subsidy

16In theory, firms may sell different products in a counterfactual scenario (e.g., no subsidy). Therefore, our exercise is apartial equilibrium exercise focusing on the price effect of the subsidy.

17Note that our estimates and draws are consistent with the observed outcome as an equilibrium. Specifically, we back outdemand shocks to fit the market share data perfectly; we invert out the marginal costs for observations in Samples (A) and (B)from the corresponding first-order conditions; and we follow the procedure described in Section 5.2 to draw the marginal costsfor observations in Sample (C), which satisfy all optimality conditions. As a result, we can directly compare the outcomes inCF1 to those in the data to quantify the effects of the subsidy.

19

Table 5 reports the price effects. We divide the simulated equilibrium retail price of each observation by

the price of the same observation in the case with no subsidy (i.e., CF1) to compute the percentage change.

We then take the average across marginal cost shock draws. We report the average across observations

within three different groups (i.e., observations for ineligible products, eligible products without binding

constraints, and eligible products with binding constraints) corresponding to Columns (1) - (3), and the

overall average price changes across all observations in Column (4) for the unweighted average and Column

(5) for the sales-weighted average.

The first row gives us the overall effect of the HAGC subsidy program. We can see that this subsidy

program with firms’ competition for subsidy eligibility leads to a reduction in retail prices for some products

while an increase for other products. Compared to a scenario without the subsidy program, prices increase

overall, with an average percentage change of 0.76% (Column (4)) and a sales-weighted average percentage

change of 1.35% (Column (5)). Examining the price changes for each subgroup of products, we find that

the retail prices of the eligible products with binding price ceilings in the data are 10.05% lower on average

(Column (3)) while other products’ prices increase on average (Columns (1) and (2)). Intuitively, when

consumers are eligible for subsidies, demand shifts to the right, and, consequently, firms are likely to raise

retail prices. The opposite effect for some products (i.e., reduction in prices) that we find indicates that

the competition for eligibility provides an incentive for firms to submit “competitive” price ceilings and thus

dampens the price increases arising from the subsidy.

We can also see this dampening effect by comparing the first row to the second row, where we remove the

price ceilings and find higher prices for all products. For example, without price ceilings, the price change for

products in Column (3) moves from -10.05% to 3.45%. Similarly, the retail price increases in Columns (1)

and (2) are smaller in the first row than in the second row. This is because prices are strategic complements

and thus the price ceilings (as a result of the competition for eligibility) not only lower the prices of the

eligible products (Columns (2) and (3)) but also reduce the prices of ineligible products (Column (1)). For

the same intuition, when the subsidy program applies to all products without price ceilings, the retail prices

increase even more (the last row). To sum up, competition for eligibility mitigates price increases due to the

subsidy and even leads to a reduction in prices for some products (compared to the retail prices without the

subsidy program).

We turn to the welfare effects in Table 6. In this table, Column (1) reports the total government

subsidy payment amount. Columns (2)-(7) present consumer and producer surplus changes (in the unshaded

rows) and their ratios to the total subsidy amount in Column (1) (in the shaded rows). Column (8) on

∆CS/(∆CS+ ∆PS) shows how the welfare change is split between consumer surplus and producer surplus.

From the row labeled “subsidy + eligible set + ceiling”, we can see that the HAGC subsidy program

increases overall consumer surplus by 3.07 billion CNY (Column (4)). Specifically, subsidy-eligible consumers

are better off by 3.70 billion CNY (Column (5)), while subsidy-ineligible consumers are worse off by 0.62

billion CNY (Column (6)). These results are consistent with the price changes shown in Table 5. Even

20

Table 5: Average Retail Price Changes (%) Compared to the Scenario without Subsidy

(1) (2) (3) (4) (5)

Subsidy + eligible set + ceiling (Data - CF1)/CF1 0.06 5.03 -10.05 0.76 1.35(<0.01) (0.64) (1.12) (0.10) (0.17)

Subsidy + eligible set (CF2 - CF1)/CF1 0.07 5.06 3.45 0.86 1.50(0.01) (0.64) (0.36) (0.11) (0.19)

Subsidy (CF3 - CF1)/CF1 2.53 5.22 3.55 2.95 4.13(0.29) (0.66) (0.37) (0.34) (0.48)

Each column is the average across the following observations based on their status in the data, i.e., under theactual HAGC subsidy program. Standard errors are reported in parentheses.

Column (1): observations for ineligible products; Column (2): observations for eligible products with no bindingconstraints; Column (3): observations for eligible products with binding constraints; Column (4): all observations,unweighted; Column (5): all observations, weighted by the observed sales units.

In all columns, we focus on markets where subsidy was in place.

Table 6: Welfare Changes Compared to the Scenario without Subsidy

(1) (2) (3) (4) (5) (6) (7) (8)

Total ∆PS ∆PS ∆CS ∆CSA ∆CSNA ∆CSR(4)

(2)Subsidy +∆CS

Subsidy + eligible set 4.54 5.84 2.77 3.07 3.70 -0.62 1.41 53%+ ceiling, (Data - CF1) (0.13) (0.24) (0.07) (0.27) (0.19) (0.08) (0.18)

129% 61% 68% 81% -14% 31%(1.76%) (2.47%) (4.10%) (2.30%) (2.05%) (3.03%)

Subsidy + eligible set 4.53 5.73 2.97 2.76 3.47 -0.71 1.25 48%(CF2 - CF1) (0.13) (0.25) (0.09) (0.32) (0.22) (0.10) (0.20)

126% 66% 61% 77% -16% 28%(2.16%) (3.26%) (5.33%) (3.03%) (2.48%) (3.53%)

Subsidy 27.41 36.40 10.26 26.14 28.34 -2.19 5.97 72%(CF3 - CF1) (1.54) (1.94) (0.58) (1.97) (1.70) (0.31) (0.85)

133% 37% 95% 103% -8% 22%(1.40%) (2.74%) (2.50%) (1.55%) (1.43%) (1.84%)

The unit of absolute numbers in white background color is billion CNY. The percentages in gray back-ground color are the ratio of the welfare change in each column to the corresponding government subsidypayment amount in Column (1). In parentheses are the standard errors, in either billion CNY or per-centages. Columns (5) - (7) are surplus changes for different subgroups of consumers, where “A” standsfor eligible consumers with agricultural Hukou, “NA” for ineligible consumers with non-agriculturalHukou, and “R” for rural consumers.

21

though firms’ competition for subsidy eligibility mitigates the price increases arising from the subsidy, the

retail prices of many products increase due to the subsidy program, leading to a decrease in the consumer

surplus for ineligible consumers. Such externalities arise from the combination of uniform prices for all

consumers and subsidies to a subgroup of consumers.18 As for the targeted population that the ”Home

Appliances Going to the Countryside” subsidy program is intended to help, i.e., the rural consumers, their

consumer surplus increases by 1.41 billion CNY.

In the end, both overall consumer surplus and producer surplus increase, with 53% of the total surplus

increase going to consumers (Column (8)). Moreover, the sum of consumer and producer surplus increases

outweighs the subsidy amount: the total surplus increase is 129% of the total government subsidy payments

(Column (2)). Therefore, under the assumption that the program leads to a tax increase and the welfare

cost of raising 1 CNY tax revenue is lower than 0.29 CNY, there is a total welfare gain in the economy under

the HAGC subsidy program.19 This is mainly driven by the mitigation of quantity distortion. Compared

to the scenario without the subsidy program, total output increases by 1.11% and total output for eligible

products increases by 8.23% under the subsidy program.

In contrast, when price ceilings are removed (the row labeled “subsidy + eligible set”), consumers, both

subsidy-eligible and ineligible ones, are worse off (i.e., their consumer surplus increases by a smaller margin

or decreases by a bigger margin, see Columns (4) to (6)) while producers are better off (i.e., produce surplus

increases by a bigger margin, see Column (2)), compared to when price ceilings are present (row “subsidy

+ eligibility + ceiling”). This is again consistent with the price change patterns shown in Table 5: prices

increase by a smaller margin with the presence of price ceilings. As a result of the smaller ∆CS and the

larger ∆PS, the ratio ∆CS/(∆CS + ∆PS) reduces to 48%, indicating that the price ceiling component of

the competition for eligibility mitigates the pass-through of subsidy from consumers to firms. Though not

reported in the table, the difference between these two rows is statistically significant across all columns.

The row “subsidy” shows that a hypothetical subsidy to all products without the competition for eligibility

would result in larger increases in all welfare measures (except for surplus for ineligible consumers due to the

greater retail price increases). However, total government subsidy payments would be 27.41 billion CNY,

six times the payments under the actual HAGC subsidy program (4.54 billion CNY). This result indicates

that specifying a set of eligible products may be necessary for making the subsidy financially feasible. In

Appendix B, we investigate an alternative policy, which is similar to CF3 except that the subsidy rate is

lower so that the total government subsidy payments remain the same.

Both the universal subsidy program in CF3 and that in Appendix B allow us to show the importance of the

eligibility competition, which results in the eligibility set and the price ceilings. As the name of the subsidy

program (“Home Appliances Going to the Countryside”) suggests, the targeted population of the subsidy

program is rural residents. Column (7) of Table 6 shows that under the universal subsidy program without

18Similar externalities are also documented in, for example, the subsidized health insurance market (Polyakova and Ryan,2021).

19The deadweight loss of the income tax in the US is estimated around 30% (Feldstein 1999).

22

the design of the eligibility competition, consumer surplus of the rural consumers increases by 22% of the

government spending. In contrast, under the subsidy program with the design of the eligibility competition,

the increase in consumer surplus of the rural consumers is 31%, about 42% higher. When comparing the

actual subsidy program to the universal subsidy program in Appendix B (i.e., a program without the design

of the eligibility competition but with the same resulting government spending), we can compare both the

level of consumer surplus change and its ratio to the government spending: the increase in consumer surplus

is 1.41 billion CNY (or 31% of the government spending) with the design vs. 0.77 billion CNY (or 17% of

the government spending) without the design, where the former is almost twice of the latter.

Overall, these results show that the competition for eligibility provides incentives for firms to submit low

price ceilings in order to be qualified for the subsidy. Such incentives lead to lower prices for all products,

including ineligible products due to the strategic complementarity of prices, and thus mitigate the price

increases arising from the subsidy (to the extent that the prices of some products even dropped). In the end,

this program design (i.e., competition for eligibility) improves the effectiveness of the program at helping its

targeted population.

7 Conclusion

In this paper, we quantify the welfare effect of a consumer subsidy program and the role of firms’ com-

petition for subsidy eligibility. We develop an estimation procedure that accommodates multiple consumer

types and binding pricing constraints. Through a set of counterfactual simulations, we find that the eligible

product set and associated price ceilings, two critical components of the competition for eligibility, mitigated

price increases under subsidy and benefited consumers and society while limiting the required government

subsidy payments.

These results suggest that a consumer subsidy can improve total welfare in an imperfectly competitive

market, and a policy can be designed to mitigate upward pricing pressure due to a subsidy, generate additional

total welfare gains, and allow consumers to take a larger share of the subsidy program’s benefits.

References

Berry, Steven, James Levinsohn, and Ariel Pakes (1995), “Automobile prices in market equilibrium.” Econo-

metrica: Journal of the Econometric Society, 841–890.

Cabral, Marika, Michael Geruso, and Neale Mahoney (2018), “Do larger health insurance subsidies benefit

patients or producers? Evidence from Medicare Advantage.” American Economic Review, 108, 2048–87.

Chen, Cheng, Shin-Yi Chou, and Robert J Thornton (2015), “The effect of household technology on weight

and health outcomes among Chinese adults: Evidence from China’s ‘Home Appliances Going to the

Countryside’ policy.” Journal of Human Capital, 9, 364–401.

23

Davis, David E (2014), “Buyer alliances as countervailing power in WIC infant-formula auctions.” Review

of Industrial Organization, 45, 121–138.

Decarolis, Francesco, Maria Polyakova, and Stephen P Ryan (2020), “Subsidy design in privately provided

social insurance: Lessons from Medicare Part D.” Journal of Political Economy, 128, 1712–1752.

Dubois, Pierre and Laura Lasio (2018), “Identifying industry margins with price constraints: Structural

estimation on pharmaceuticals.” American Economic Review, 108, 3685–3724.

Fan, Ying and Chenyu Yang (2020), “Competition, product proliferation, and welfare: A study of the US

smartphone market.” American Economic Journal: Microeconomics, 12, 99–134.

Feldstein, Martin (1999), “Tax avoidance and the deadweight loss of the income tax.” Review of Economics

and Statistics, 81, 674–680.

Gandhi, Amit and Jean-Francois Houde (2019), “Measuring substitution patterns in differentiated products

industries.” NBER Working Paper w26375.

Goldberg, Pinelopi Koujianou (1995), “Product differentiation and oligopoly in international markets: The

case of the US automobile industry.” Econometrica: Journal of the Econometric Society, 891–951.

Oliveira, Victor, Elizabeth Frazao, David Smallwood, et al. (2010), “Rising infant formula costs to the WIC

program: recent trends in rebates and wholesale prices.” Economic Research Report-Economic Research

Service, USDA.

Pakes, Ariel, Jack Porter, Kate Ho, and Joy Ishii (2015), “Moment inequalities and their application.”

Econometrica, 83, 315–334.

Pless, Jacquelyn and Arthur A van Benthem (2019), “Pass-through as a test for market power: An application

to solar subsidies.” American Economic Journal: Applied Economics, 11, 367–401.

Polyakova, Maria and Stephen P Ryan (2021), “Subsidy targeting with market power.” NBER Working

Paper w26367.

Sallee, James M (2011), “The surprising incidence of tax credits for the Toyota Prius.” American Economic

Journal: Economic Policy, 3, 189–219.

Sinkinson, Michael (2020), “Pricing and entry incentives with exclusive contracts.” Unpublished manuscript.

Tewari, Ishani and Yabin Wang (2020), “Durable ownership, time allocation and female labor force partic-

ipation: Evidence from China’s ‘Home Appliances to the Countryside’ rebate.” Economic Development

and Cultural Change, forthcoming.

Wang, Fei-Ling (2014), The Hukou (household registration) system. Oxford University Press.

Wang, Peichun (2020), “Product portfolio choices with product life cycles.” Unpublished manuscript.

Weyl, E Glen and Michal Fabinger (2013), “Pass-through as an economic tool: Principles of incidence under

imperfect competition.” Journal of Political Economy, 121, 528–583.

Zhu, Ting, Hongju Liu, and Pradeep K Chintagunta (2015), “Wireless carriers’ exclusive handset arrange-

ments: An empirical look at the iPhone.” Customer Needs and Solutions, 2, 177–190.

24

A Appendix: Sample Construction

We construct our sample for analysis as follows. We first drop observations from Beijing, Shanghai, Tibet,

and online sales. Beijing and Shanghai have only a small share of consumers eligible to claim the HAGC

subsidy and thus are not very relevant to our analysis of the subsidy program. Moreover, consumers in such

super metropolises may have different preferences on cell phones. At the other extreme, Tibet has a very

small population and very low cell phone sales, leading to imprecise measures of the average prices reported

by GfK. Finally, we drop online sales because our data source reports online sales only at the national level

without providing a breakdown at the province level. Overall, the online sales account for 8.75% of the total

sales units in the full sample.

We aggregate the data from the original monthly level to the quarterly level by summing up the sales

units and taking the sales-weighted average for prices.20 We do so because quarterly sales are measured

more precisely than monthly ones. We then drop an observation (a product/province/quarter combination)

if its number of sales units is no larger than 500 or accounts for less than 0.1% of the total sales units in that

province and quarter. We also drop a product if its price is always above 2,000 CNY in the sample. The

HAGC-eligible products are mostly low-end products priced below 1,000 CNY. Thus, the high-end products

and their targeted consumers have little influence on the welfare analysis of the subsidy program for low-end

products. Finally, we drop an observation if the product is released or discontinued in the quarter because

the sales in such cases are highly subject to (unobserved) product inventory and do not necessarily reflect

underlying consumer preferences. All these dropped products are part of the outside option.

B Appendix: Alternative Subsidy Policy Designs

This appendix presents the welfare results for an alternative subsidy policy that is similar to that in CF3.

We have seen in Section 6 that the policy in CF3, i.e., a universal subsidy at the actual 13% rate (of the

retail price up to a maximum subsidy of 130 CNY), would result in subsidy payments that might not be

financially feasible. In this appendix, we consider a universal subsidy at a 1.96% rate instead (CF4). We

calibrate the rate to be 1.96% so that the total subsidy payment amount is the same as that under the actual

policy. We consider that only consumers with agricultural Hukou are eligible for the subsidy, the same as

in the actual policy. We report the welfare effects of this alternative subsidy policy and compare them with

those of the actual subsidy in Table B.1.

The results indicate that the hypothetical 1.96% universal subsidy would bring higher overall consumer

surplus gains than the actual policy. However, as we discuss in Section 2.3 and as the name “Home Appliances

Going to the Countryside” implicates, the HAGC subsidy program aimed to help consumers from rural areas

despite that the subsidy eligibility was based on Hukou type as a proxy of rural residence. We find that the

20The three months in a quarter may not belong to the same round of HAGC subsidy. In such cases, we aggregate the twomonths belonging to the same round into one observation and keep the other single month as a separate observation. We makecorresponding adjustments when calculating market shares. For simplicity, we still use “quarter” to refer to such observations.

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consumers in the rural area, the real target of the HAGC subsidy program, would have larger welfare gain

under the actual program (1.41 billion CNY) than under the hypothetical 1.96% universal one (0.77 billion

CNY). These results are intuitive since the government selected the products that best met the needs of

targeted consumers and was able to offer the 13% (much higher than 1.96%) subsidy rate by restricting to

a smaller range of eligible products.

Therefore, which policy design is better depends on the government’s objective function. For example,

suppose the government puts a relatively large weight on the welfare of consumers in the rural area. In that

case, it should choose the actual policy design with selected eligible products (together with price ceilings

and a higher subsidy rate) over the hypothetical 1.96% universal one according to our simulation results.21

Table B.1: Welfare Changes Compared to the Scenario without Subsidy: An Alternative Subsidy Policy

(1) (2) (3) (4) (5) (6) (7) (8)Total ∆PS ∆PS ∆CS ∆CSA ∆CSNA ∆CSR (4)/(2)

Subsidy +∆CS

Actual subsidy program 4.54 5.84 2.77 3.07 3.70 -0.62 1.41 53%(Data - CF1) (0.13) (0.24) (0.07) (0.27) (0.19) (0.08) (0.18)

129% 61% 68% 81% -14% 31%(1.76%) (2.47%) (4.10%) (2.30%) (2.05%) (3.03%)

Universal subsidy of 1.96% 4.54 6.14 2.05 4.09 4.78 -0.69 0.77 67%(CF4 - CF1) (0.06) (0.29) (0.07) (0.27) (0.18) (0.08) (0.10)

135% 45% 90% 105% -15% 17%(4.72%) (1.17%) (4.74%) (2.85%) (2.01%) (1.87%)

The unit of absolute numbers in white background color is billion CNY. The percentages ingray background color are the ratio of the welfare change in each column to the correspondinggovernment subsidy payment amount in Column (1). In parentheses are the standard errors, ineither billion CNY or percentages. Columns (5) - (7) are surplus changes for different subgroups ofconsumers, where “A” stands for eligible consumers with agricultural Hukou, “NA” for ineligibleconsumers with non-agricultural Hukou, and “R” for rural consumers.

C Appendix: Summary Statistics by Sub-samples

In this appendix, we present the summary statistics for Samples (A)–(C) separately in Table C.2. The

table shows significant overlaps across these three sub-samples in product characteristics, retail prices, and

sales. We also note that Sample (A), based on which we estimate the marginal cost parameters and the

distribution of the marginal cost shocks, covers all firms in our sample.

21There are some other operational reasons (that are not in the scope of our economic analysis) for not expanding the subsidyto all products. For example, the government did quality examinations on each participating cell phone model to ensure itwould meet the needs of eligible consumers, which would be less practicable for all the thousands of models. Limiting the setof eligible products also made it easier for the government to prevent abuse and fraud in the rebate redemption.

26

Table C.2: Summary Statistics by Sub-samples

Sub-sample (A) (B) (C)Mean Std Min Max Mean Std Min Max Mean Std Min Max

Number of units sold 6,263 14,205 500 893,457 7,307 13,958 500 492,631 5,649 10,976 501 226,778Retail price (1,000 CNY) 1.02 0.62 0.11 3.00 0.95 0.64 0.12 3.00 1.00 0.67 0.14 3.00Smartphone 0.29 0.19 0.18Include camera 0.80 0.73 0.73Include touch screen 0.36 0.26 0.23Support 3G network 0.33 0.27 0.21Dual SIM card 0.16 0.08 0.08Design: flip 0.11 0.08 0.07Design: slider 0.13 0.22 0.24Storage memory (GB) 1.16 1.23 0.01 16.00 0.96 0.84 0.01 16.00 0.89 0.59 0.02 15.63Camera resolution (MP) 2.07 1.66 0.10 12.00 1.87 1.26 0.10 12.00 1.84 1.18 0.10 8.00Handset size (inch) 4.73 0.41 2.88 8.74 4.59 0.29 3.63 6.00 4.56 0.28 3.63 5.88

Number of observations 61,688 29,778 6,980

27

Dependent variable pjmt − pj Market share (%)

Sample Full Exclude Ever Full Exclude Ever

sample binding binding sample binding binding

1(subsidy in place)mt × 1(eligible)jmt 0.009** 0.010** -0.012 0.021** 0.022** 0.001

(0.002) (0.003) (0.005) (0.002) (0.002) (0.008)

1(subsidy in place)mt × 1(ineligible)jmt -0.004 -0.004 0.014 -0.006** -0.006** -0.003

(0.002) (0.002) (0.005) (0.001) (0.001) (0.008)

FEs for provinces, quarters, firms Yes Yes Yes Yes Yes Yes

Observations 98,446 97,993 9,203 98,446 97,993 9,203

** p<0.01, * p<0.05

28